I'm going to be adopting a cat to travel with me once I'm more secure in my financial ability to do so. I've already lived in my RV with my best friend and her cat for about 3 months last year although we weren't doing any traveling at that time.
As a certified Veterinary Technician with experience working in a vet clinic, I'd be real nervous about letting a cat ride in a TT while in motion. If you were to have to step on the breaks suddenly and the pet isn't secured in a carrier the poor thing could go flying and get hurt. Likewise, there's not a good way to keep a TT climate controlled while driving, it could get real hot inside in the summer with the sun beating down on the TT, and you can't really keep a window open without road debris getting inside.
Just my two cents.